Let's take a look at the bigger picture for a moment, maybe?
The Cold War, which was itself just the latest iteration of the Great Game. There was the USA, and there was the USSR, and all of the world was either in one camp or the other. In the Middle-east, just like everywhere else on Earth, some countries were US proxies, and some were Soviet proxies.
That is the bigger context in which the entire existence of the modern state of Israel should be seen, and also the current "theocratic" state of Iran.
The Shah of Iran was a Western puppet - as someone else mentioned, not too good a puppet... if as Monk said, even freaking Jimmy Carter was willing to depose him for someone more pliant, that just shows how much the USA's attitude to the rest of the world has long been all about what's good for American Big Business. Democracy? A people's freedom to have a leader of their own choice? LOL no, muh interests.
Except that the Other Side got in first and put a Comrade in robes and a turban in the place of the Shah. Islamic Revolution?
(okay, I have some "hot takes" sometimes)
And of course let's not for moment imagine that the cold calculating minds in the Kremlin cared much about what was good for the Iranian people either.